Ising systems, measures on the sphere, and zonoids

DOI10.2140/tunis.2024.6.299zbMATH Open1546.49022MaRDI QIDQ6589647

A. Chambolle, Andrea Braides

Publication date: 20 August 2024

Published in: Tunisian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

homogenizationGamma-convergenceperimeter functionalsIsing systemszonoidsdiscrete-to-continuum

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Inequalities and extremum problems involving convexity in convex geometry (52A40) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Optimization of shapes other than minimal surfaces (49Q10) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

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• Approximation of free-discontinuity problems
• Design of lattice surface energies
• Approximation of zonoids by zonotopes
• Homogenization of surface and length energies for spin systems
• Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem
• Sets of Finite Perimeter and Geometric Variational Problems
• Finite-differences discretizations of the mumford-shah functional
• Convex Bodies The Brunn-MinkowskiTheory
• Geometric Flows on Planar Lattices
• Discrete Variational Problems with Interfaces
• Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems

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